# How do you solve the system of equations and enter the solution as an ordered pair 7x - 5y = 31 and 4x - 7y = -3?

Apr 8, 2018

$x = 8$ and $y = 5$

#### Explanation:

7x - 5y = 31 color(white)(...)……(1)
4x - 7y = -3 color(white)(...) …….(2)

Multiply first equation by $7$ and second equation by $5$
Now, we have

$49 x - 35 y = 217$
$20 x - 35 y = - 15$

Subtract second equation from first one

$\left(49 x - 35 y\right) - \left(20 x - 35 y\right) = 217 - \left(- 15\right)$

$49 x - 35 y - 20 x + 35 y = 217 + 15$

$49 x - 20 x = 232$

$29 x = 232$

$x = \frac{232}{29}$

$\textcolor{b l u e}{x = 8}$

Substitute $x = 8$ in equation $\left(1\right)$

$7 \left(8\right) - 5 y = 31$

$56 - 5 y = 31$

$5 y = 56 - 31$

$y = \frac{56 - 31}{5}$

$\textcolor{b l u e}{y = 5}$